Spline collocation for strongly elliptic equations on the torus
Identifieur interne : 001E60 ( Istex/Corpus ); précédent : 001E59; suivant : 001E61Spline collocation for strongly elliptic equations on the torus
Auteurs : Martin Costabel ; William McleanSource :
- Numerische Mathematik [ 0029-599X ] ; 1992-12-01.
English descriptors
- KwdEn :
- Asymptotic convergence, Boundary integral operators, Classical boundary integral operators, Coefficient, Collocation, Collocation equations, Collocation method, Collocation methods, Collocation points, Collocation scheme, Convergence, Costabel, Double layer, Elliptic, Elliptic equations, Elliptic pseudodifferential operators, Error analysis, Error estimate, Fourier, Fourier coefficients, Higher dimensions, Highest convergence rate, Iiun, Integral equations, Local approximation property, Local principle, Mclean, Midpoint collocation, Numerical solution, Plane case, Potential theory, Pr6bdorf, Principal symbol, Principal symbols, Pseudodifferential, Pseudodifferential operator, Pseudodifferential operators, Sect, Single layer, Singular integral equations, Spline, Spline collocation, Spline collocation methods, Strong ellipticity, Torus, Wendland.
- Teeft :
- Asymptotic convergence, Boundary integral operators, Classical boundary integral operators, Coefficient, Collocation, Collocation equations, Collocation method, Collocation methods, Collocation points, Collocation scheme, Convergence, Costabel, Double layer, Elliptic, Elliptic equations, Elliptic pseudodifferential operators, Error analysis, Error estimate, Fourier, Fourier coefficients, Higher dimensions, Highest convergence rate, Iiun, Integral equations, Local approximation property, Local principle, Mclean, Midpoint collocation, Numerical solution, Plane case, Potential theory, Pr6bdorf, Principal symbol, Principal symbols, Pseudodifferential, Pseudodifferential operator, Pseudodifferential operators, Sect, Single layer, Singular integral equations, Spline, Spline collocation, Spline collocation methods, Strong ellipticity, Torus, Wendland.
Abstract
Summary: We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4].
Url:
DOI: 10.1007/BF01396241
Links to Exploration step
ISTEX:A198D8E207D1056E9BBC92945A9F696146261D9ALe document en format XML
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Math.</title><idno type="pISSN">0029-599X</idno><idno type="eISSN">0945-3245</idno><idno type="journal-ID">true</idno><idno type="issue-article-count">27</idno><idno type="volume-issue-count">0</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>Berlin/Heidelberg</pubPlace><date type="published" when="1992-12-01"></date><biblScope unit="volume">62</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="511">511</biblScope><biblScope unit="page" to="538">538</biblScope></imprint></monogr></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1990-12-28</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Summary: We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. 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Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4].</Para></Abstract><KeywordGroup Language="En"><Heading>Mathematics Subject Classification (1991)</Heading><Keyword>65R20 (35S15</Keyword><Keyword>41A15</Keyword><Keyword>41A63</Keyword><Keyword>65N35</Keyword></KeywordGroup></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Spline collocation for strongly elliptic equations on the torus</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Spline collocation for strongly elliptic equations on the torus</title></titleInfo><name type="personal" displayLabel="corresp"><namePart type="given">Martin</namePart><namePart type="family">Costabel</namePart><affiliation>Département de Mathématiques, Université Bordeaux 1, 351 cours de la Libération, F-33405, Talence Cédex, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">William</namePart><namePart type="family">McLean</namePart><affiliation>School of Mathematics, University of New South Wales, Sydney, Australia</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Springer-Verlag</publisher><place><placeTerm type="text">Berlin/Heidelberg</placeTerm></place><dateCreated encoding="w3cdtf">1990-12-28</dateCreated><dateIssued encoding="w3cdtf">1992-12-01</dateIssued><dateIssued encoding="w3cdtf">1992</dateIssued><copyrightDate encoding="w3cdtf">1992</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Summary: We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4].</abstract><classification displayLabel="Mathematics Subject Classification (1991)">65R20 (35S15</classification><classification displayLabel="Mathematics Subject Classification (1991)">41A15</classification><classification displayLabel="Mathematics Subject Classification (1991)">41A63</classification><classification displayLabel="Mathematics Subject Classification (1991)">65N35</classification><relatedItem type="host"><titleInfo><title>Numerische Mathematik</title></titleInfo><titleInfo type="abbreviated"><title>Numer. Math.</title></titleInfo><genre type="journal" displayLabel="Archive Journal" authority="ISTEX" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre><originInfo><publisher>Springer</publisher><dateIssued encoding="w3cdtf">1992-12-01</dateIssued><copyrightDate encoding="w3cdtf">1992</copyrightDate></originInfo><subject><genre>Mathematics</genre><topic>Mathematics, general</topic><topic>Numerical Analysis</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Numerical and Computational Methods</topic><topic>Appl.Mathematics/Computational Methods of Engineering</topic></subject><identifier type="ISSN">0029-599X</identifier><identifier type="eISSN">0945-3245</identifier><identifier type="JournalID">211</identifier><identifier type="IssueArticleCount">27</identifier><identifier type="VolumeIssueCount">0</identifier><part><date>1992</date><detail type="volume"><number>62</number><caption>vol.</caption></detail><detail type="issue"><number>1</number><caption>no.</caption></detail><extent unit="pages"><start>511</start><end>538</end></extent></part><recordInfo><recordOrigin>Springer-Verlag, 1992</recordOrigin></recordInfo></relatedItem><identifier type="istex">A198D8E207D1056E9BBC92945A9F696146261D9A</identifier><identifier type="ark">ark:/67375/1BB-7PV5B041-F</identifier><identifier type="DOI">10.1007/BF01396241</identifier><identifier type="ArticleID">BF01396241</identifier><identifier type="ArticleID">Art25</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag, 1992</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</recordContentSource><recordOrigin>Springer-Verlag, 1992</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/document/A198D8E207D1056E9BBC92945A9F696146261D9A/metadata/json</uri></json:item></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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